Prove that the sum of two fourth powers of integers can never be three more than a multiple of 4. In other words, prove that it is not possible for n4+ m4= 4k+3, for integers n,m, and k. [Hint: consider fourth powers of even and odd integers.
Prove that the sum of two fourth powers of integers can never be three more than a multiple of 4. In other words, prove that it is not possible for n4+ m4= 4k+3, for integers n,m, and k. [Hint: consider fourth powers of even and odd integers.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 14OE
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Prove that the sum of two fourth powers of integers can never be three more than a multiple of 4. In other words, prove that it is not possible for n4+ m4= 4k+3, for integers n,m, and k. [Hint: consider fourth powers of even and odd integers.
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